David Cameron has suggested firms should allow parents to take their children to work on the day that millions of public sector workers strike over pensions next Wednesday.

The prime minister told MPs in the Commons that the industrial action scheduled for 30 November was the "height of irresponsibility" on a day that he urged members to defy the strikes to avoid inflicting "pain" on hardworking people "who pay your wages".

Louise Mensch, Tory MP for Corby and East Northamptonshire, asked Cameron during prime minister's questions whether he thought people should take their kids to work with them to minimise disruption to their day.

Cameron told MPs: "These strikes are going to go ahead. Everyone should be very clear about where responsibility lies. It is with those union leaders and … the party opposite … but I think she makes an important point that where it is safe to help people bring their children to work then I think organisations should do so."

Tory colleagues asked Cameron a series of questions about the mass action scheduled for next week that will result in most schools being forced to close after the main education unions balloted members.

He said the planned walkout by millions of teachers, civil servants and other public sector workers was a "tragedy" at a time when an "extremely reasonable" pensions offer was on the table.

"It really is irresponsible, when negotiations are ongoing, to call strikes that will actually lead to the closure of most of the classrooms in our country," he said.

"It's the height of irresponsibility. I have to say, what is on offer is an extremely reasonable deal – low and middle earners getting a larger pension at retirement than now, all existing accrued rights being fully protected, any worker within 10 years of retirement seeing no change in either the age they can retire or the amount they can receive.

He challenged the Labour leader, Ed Miliband, to condemn the mass walkout, which he conceded would "lead to the closure of most of the classrooms in the country".

"I think also it is a tragedy that it is not just the union leaders that don't understand this but the party opposite refuses to condemn these strikes."

The Labour leader has previously said he thought strikes while public sector pension negotiations were still going on is a "mistake", and that strikes show a failure on both sides of the talks.

Cameron suggested in a column in the Sun that the strikes lack support from public sector workers as he urged members to cross the picket line and go to work.

"I'm so angry union bosses are ordering millions of public sector workers to strike next week – even while talks are under way. Most of them did not vote for this. Only a quarter of union members backed industrial action."

Ballots conducted by public sector unions taking part in the action have resulted in a range of turnouts but the traditionally more moderate unions have recorded the highest proportions of members voting.

While Unite had a turnout of 31%, the FDA, representing senior civil servants, including Whitehall mandarins and diplomats — which has never been on strike before – saw 81% back action on a turnout of 54%. Prospect, the civil service union, had a turnout of 52%.

Michael Dugher, Labour's shadow minister without portfolio, said both unions and government must "give ground" if a deal is to be reached.

"Everyone's concern now must be to avoid the hardship and disruption that will be caused for millions of families who rely on public services if these strikes go ahead," he said.

"But rather than telling hundreds of thousands of low paid, part-time working women who are set to be much worse off that they should not strike, David Cameron should be taking responsibility and trying to negotiate a deal that's fair to low paid workers and taxpayers alike.

"The government must bear much of the responsibility for what is happening because it jumped the gun and effectively imposed a 3% tax on public sector workers and then refused to negotiate on this. This surcharge is going straight to the Treasury and has nothing to do with the sustainability of public sector pensions.

"Even at this late stage, we urge both sides to exhaust every possible avenue to avoid industrial action. But ramping up the rhetoric and refusing to negotiate on key issues is not going to help avoid next week's strike."

The Guardian reported on Wednesday that UK Border Agency staff in embassies around the world are being offered flight homes to provide cover during next week's strike.

EU civil servants have backed strike calls over plans to give them a pay rise of 1.8% and increase their working week to 40 hours.

The prime minister's spokesman refused to comment directly on reports that the UK Border Agency is spending public money to fly in extra immigration staff from India, South Africa and Russia. But he said: "The public would expect us to do what we can to mitigate the effect of the strikes."

Cameron and Miliband also clashed over youth unemployment in the light of figures published last week that show more than 1 million 16-24-year-olds are now out of work.

The Labour leader claimed Cameron regarded unemployment as a "price worth paying to protect his failed plan" and called on him to impose a tax on bank bonuses to pay for youth job creation schemes.

Miliband said Cameron must change course on his economic strategy or risk a "lost generation" of unemployed youngsters becoming the symbol of his time in office.

"You were warned that your strategy of cutting too far and too fast wouldn't create jobs, you were warned it wouldn't create growth and you were warned you would find it harder to get the deficit down," he said. "Isn't that exactly what has happened?"

But Cameron insisted the UK was growing faster than the European average and warned that a change in approach could lead to increased interest rate rises.

He added: "That is the risk that we would have with Labour's plans for more spending, more borrowing and more debt."